Now officers want to hear from members of the public who may have vital information relating to their investigation.

Detective Inspector Martin Fergus, major investigation teams, said: “We are currently following a number of lines of enquiry regarding both incidents – we need to do is establish what happened between 8pm on Wednesday, June 8 when Ms Douglas was last seen and 6am on Thursday morning when she was found.

“To this end, I would appeal to anyone who was in the area, who may have seen any suspicious activity – whether that be a vehicle or someone on foot in the area – to contact police.”

Police are still trying to determine how and why the fire at Peacockbank Farm started, with a joint investigation between police and Scottish Fire and Rescue now underway.

Anyone with information about the murder or the fire is asked to contact the incident room in Kilmarnock on a new incident room number, 01563 505 172, or via 101.

Crimestoppers can be reached on 0800 555 111 where details can be given in confidence.